PDQ Algorithm: Infinite precision best fraction within tolerance

[Joe Horn]

(05-01-2015 01:54 AM)compsystems Wrote:  Great program! which means the acronym PDQ?

Thanks. Two meanings: (1) Since the math literature often uses P/Q when talking about continued fractions, I wanted to call the original HP48 function 'P/Q' but the parser didn't like that name, so I called it 'PDQ' with "D" standing for "Divide". (2) It's a common English abbreviation for "Pretty Darn Quick" (or equivalent words for "D"), and is used as a synonym for "immediately" or "at once", as in "Get that project started PDQ!". It's ASAP on steroids. Since the PDQ Algorithm is so fast, it seemed an appropriate name. No relation to PDQ Bach, unfortunately.

(05-01-2015 01:54 AM)compsystems Wrote:  A question, should be called arbitrary presicion, there tolerance. The tolerance parameter makes it finite.

Counterintuitively, in English "infinite precision" and "arbitrary precision" are more or less synonyms. That's why "Infinite Precision" in Wikipedia defaults to the "Arbitrary Precision" page: http://en.wikipedia.org/w/index.php?titl...edirect=no

I prefer "infinite precision" in this case because the user-specified precision is not limited by the algorithm or by the machine's floating-point bandwidth, but only by available memory. "Infinite precision" is never really infinite of course; it's just what it's called.

(05-01-2015 01:54 AM)compsystems Wrote:  Please can port this code into the HP50G

Done, long ago, in System RPL for speed. It was the subject of my HHC 2003 presentation (on the 49G at the time, I think). I'll post the 50g program to the "General Software Library" ASAP, if not PDQ.

EDIT: Done. The 50g version is HERE.